Subdividing part of spherical object without getting weird bumps
Assuming a couple of levels of subdivision below those already applied, a fairly conventional method to insert features like this into curved surfaces is to use a topology something like this:

 

Retain an intact,featureless, more subdivided copy of the sphere in the same place, and assign a Shrinkwrap modifier to your model with the intact sphere as target. (You can hide the target sphere, or put it on another layer) 

Make a vertex group in your model, of all the vertices you want to conform to the target surface, (for example, excluding the ones shaded blue in the picture) and aim the Shrinkwrap at that group.

The result:



Matcap - showing Srinkwrap off:



Matcap - showing Srinkwrap on: